On (m,n)-ideals of Left Almost Semigroups

Abstract

In this paper, we study (m,n)-ideals of an LA-semigroup in detail. We charactrize (0,2)-ideals of an LA-semigroup S and prove that A is a (0,2)-ideal of S if and only if A is a left ideal of some left ideal of S. We also show that an LA-semigroup S is 0-(0,2)-bisimple if and only if S is right 0-simple. Furthermore we study 0-minimal (m,n)-ideals in an LA-semigroup S and prove that if R (L) is a 0-minimal right (left) ideal of S, then either R^{m}Lâ¿={0} or R^{m}Lâ¿ is a 0-minimal (m,n)-ideal of S for m,n≥3. Finally we discuss (m,n)-ideals in an (m,n)-regular LA-semigroup S and show that S is (0,1)-regular if and only if L=SL where L is a (0,1)-ideal of S.